A Multivariate Analysis of Freeway Speed and Headway Data

The knowledge of speed and headway distributions is essential in microscopic traffic flow studies because speed and headway are both fundamental microscopic characteristics of traffic flow. For microscopic simulation models, one key process is the generation of entry vehicle speeds and vehicle arrival times. It is helpful to find desirable mathematical distributions to model individual speed and headway values, because the individual vehicle speed and arrival time in microscopic simulations are usually generated based on some form of mathematical models. Traditionally, distributions for speed and headway are investigated separately and independent of each other. However, this traditional approach ignores the possible dependence between speed and headway.

To address this issue, the dissertation presents two different methodologies to construct bivariate distributions to describe the characteristics of speed and headway. Based on the investigation of freeway speed and headway data measured from the loop detector data on IH-35 in Austin, it is shown that there exists a weak dependence between speed and headway and the correlation structure can vary depending on the traffic condition.

The dissertation first proposes skew-t mixture models to capture the heterogeneity in speed distribution. Finite mixture of skew-t distributions can significantly improve the goodness of fit of speed data. To develop a bivariate distribution to capture the dependence and describe the characteristics of speed and headway, finite mixtures of multivariate skew-t distributions are applied to the 24-hour speed and headway data. The bivariate skew-t mixture model can provide a satisfactory fit to the multimodal speed and headway distribution and this modeling approach can accommodate the varying correlation structure between speed and headway.

To avoid the restriction of the bivariate skew-t distributions that individual behavior of speed and headway is described by the same univariate distributions, this research proposes copulas as an alternative method for constructing the multivariate distribution of traffic variables. Copula models can adequately represent the multivariate distributions of microscopic traffic data and accurately reproduce the dependence structure revealed by the speed and headway observations. This dissertation compares the advantages and disadvantages of copula models and finite mixtures of multivariate distributions. Overall, the proposed methodologies in this dissertation can be used to generate more accurate vehicle speeds and vehicle arrival times by considering their dependence on each other when developing microscopic traffic simulation models.